Direct position determination with phase error compensation for multiple targets using spatial sparsity

Measuring the positions of multiple targets is key in many positioning applications. Utilizing compressed sensing theory, measurements using the sparse direct position determination (DPD) methods are more accurate than the two-step methods and the traditional DPD methods. Position measurement with mobile access points (APs) expands the network coverage, increases information throughput and reduces implementation costs, which motivates us to extend sparse DPD (SDPD) to the mobility-assisted positioning system. However, one of the most critical problems in mobility-assisted positioning is the model errors coming from the AP position and velocity uncertainty. The paper proposes a phase error compensation algorithm for the SDPD algorithm based on mobile APs. The algorithm makes two key technical contributions. First, a double iteration for l(2,1)-norm optimization is designed to compensate phase errors and recover target distribution maps simultaneously. Second, when the data collection is incomplete or irregular, the algorithm jointly integrates the global information of target distribution maps at different APs to improve the measurement accuracy. Experimental results indicate the effectiveness of the algorithm.